You can get it fixed, but the Sony VAIO is trouble, the parts are expensive and very difficult to get, and skilled VAIO repair people are rare. It could be something as simple as a hard drive or memory which are easy to replace cheaply. But it could be a power supply or LCD inverter which commonly fail in the VAIOS, and are expensive and difficult to repair.
Wisest move is to pay $55 for a full analysis by a skilled, certified, laptop technian. Then decide what to do based on the estimate.
A new hard drive you can replace yourself, if you have the recovery disk set to help you.
First, though, do ANY lights come on. Does the fan turn at all...even a quarter of a turn when you press the on button. Is the power adapter damaged in any way? Are the power adapter cables smooth or lumpy. Has the computer had any impact from the side or back. Has it been dropped by more than 14 inches?
There are ways to narrow it down with answers to these questions.